Statistical Analysis Final Exam

Parameters are

numerical characteristics of a population

Larger values of the standard deviation result in a normal curve that is

wider and flatter

Which of the following is not a characteristic of the normal probability distribution?

The standard deviation must be 1

A negative value of Z indicates that

the number of standard deviations of an observation is to the left of the mean

The probability distribution of all possible values of the sample proportion Pbar is the

sampling distribution of Pbar

The center of a normal curve is

is the mean of the distribution

In a standard normal distribution, the mean is what

mean is 0 and the standard deviation is 1

In a standard normal distribution, the probability that Z is greater than zero is

0.5

For a continuous random variable x, the height of the function at x is

named the probability density function f(x)

A theorem that allows us to use the normal probability distribution to approximate the sampling distribution of sample means and sample proportions whenever the sample size is large is known as the

central limit theorem

A standard normal distribution is a normal distribution

with a mean of 0 and a standard deviation of 1

A simple random sample from an infinite population is a sample selected such that

each element is selected independently and from the same population

Which of the following is an example of nonprobabilistic sampling?

judgment sampling

Stratified random sampling is a method of selecting a sample in which

the population is first divided into strata, and then random samples are drawn from each stratum

In point estimation

data from the sample is used to estimate the population parameter

A sample of 92 observations is taken from an infinite population. The sampling distribution of Xbar is approximately

normal because of the central limit theorem

As the sample size increases, the variability among the sample means

decreases

A simple random sample of 28 observations was taken from a large population. The sample mean equaled 50. Fifty is a

point estimate

For any continuous random variable, the probability that the random variable takes avalue less than zero

is any number between zero and 1

Convenience sampling is an example of

nonprobabilistic sampling

The probability that a continuous random variable takes any specific value

is equal to zero

As the sample size becomes larger, the sampling distribution of the sample mean approaches a

normal distribution

As the sample size increases, the

standard error of the mean decreases

Sampling distribution of Xbar is the

probability distribution of the sample mean

The z score for the standard normal distribution

can be either negative or positive

A finite population correction factor is needed in computing the standard deviation of the sampling distribution of sample means

whenever the sample size is more than 5% of the population size

Whenever the population has a normal probability distribution, the sampling distribution of Xbar is a normal probability distribution for

any sample size

In computing the standard error of the mean, the finite population correction factor is used when

n/N > 0.05

For a normal distribution, a positive value of z indicates that

the sample mean is larger than the population mean

For any continuous random variable, the probability that the random variable takes on exactly a specific value is

almost zero

Which of the following is not a characteristic of the normal probability distribution?

99.72% of the time the random variable assumes a value within plus or minus 1 standard deviation of its mean

The standard deviation of a normal distribution

cannot be negative

Since the sample size is always smaller than the size of the population, the sample mean

can be smaller, larger, or equal to the population mean

A simple random sample from an infinite population is a sample selected such that

each element is selected independently and from the same population

A subset of a population selected to represent the population is

a sample

An estimate of a population parameter that provides an interval of values believed to contain the value of the parameter is known as the

interval estimate

In order to use the normal distribution for interval estimation of m when s is known and the sample is very small, the population

must have a normal distribution

In interval estimation, as the sample size becomes larger, the interval estimate

becomes narrower

The value added and subtracted from a point estimate in order to develop an interval estimate of the population parameter is known as the

margin of error

After computing a confidence interval, the user believes the results are meaningless because the width of the interval is too large. Which one of the following is the best recommendation?

Increase the sample size.

If we change a 95% confidence interval estimate to a 99% confidence interval estimate, we can expect

the size of the confidence interval to increase

In general, higher confidence levels provide

wider confidence intervals

Whenever using the t distribution for interval estimation (when the sample size is very small), we must assume that

the population is approximately normal

When constructing a confidence interval for the population mean and the standard deviation of the sample is used, the degrees of freedom for the t distribution equals

n-1

When the level of confidence decreases, the margin of error

becomes smaller

The p-value

is a probability

The sampling distribution of Pbar1-Pbar2 is approximated by a

normal distribution

The p-value is a probability that measures the support (or lack of support) for the

null hypothesis

For a lower tail test, the p-value is the probability of obtaining a value for the test statistic

at least as small as that provided by the sample

An assumption made about the value of a population parameter is called a

hypothesis

Which of the following does not need to be known in order to compute the p-value?

the level of significance

The p-value

must be a number between zero and 1

The level of significance is the

maximum allowable probability of Type I error

When the p-value is used for hypothesis testing, the null hypothesis is rejected if

p-value <= a

In hypothesis testing, the tentative assumption about the population parameter is

the null hypothesis

To construct an interval estimate for the difference between the means of two populations when the standard deviations of the two populations are unknown and it can be assumed the two populations have equal variances, we must use a t distribution with (let n1 be the size of sample 1 and n2 the size of sample 2)

(n1 + n2 - 2) degrees of freedom

When developing an interval estimate for the difference between two sample means, with sample sizes of n1 and n2,

n1 and n2 can be of different sizes

In hypothesis testing if the null hypothesis is rejected,

the alternative hypothesis is true

The probability of committing a Type I error when the null hypothesis is true is

the Level of Significance

The probability of making a Type I error is denoted by

a

The standard error of Xbar1-Xbar2 is the

standard deviation of the sampling distribution of Xbar1-Xbar2

When each data value in one sample is matched with a corresponding data value in another sample, the samples are known as

matched samples

To compute an interval estimate for the difference between the means of two populations, the t distribution

is not restricted to small sample situations

If we are interested in testing whether the proportion of items in population 1 is larger than the proportion of items in population 2, the

alternative hypothesis should state P1 - P2 > 0

The symbol used for the variance of the sample is

S2

For an F distribution, the number of degrees of freedom for the numerator

can be larger, smaller, or equal to the number of degrees of freedom for the denominator

If two independent large samples are taken from two populations, the sampling distribution of the difference between the two sample means

can be approximated by a normal distribution

The sampling distribution of the ratio of independent sample variances extracted from two normal populations with equal variances is the

Z distribution

When developing an interval estimate for the difference between two sample means, with sample sizes of n1 and n2,

n1 and n2 can be of different sizes

Independent simple random samples are taken to test the difference between the means of two populations whose variances are not known, but are assumed to be equal. The sample sizes are n1 = 32 and n2 = 40. The correct distribution to use is the

t distribution with 70 degrees of freedom

The sampling distribution of the ratio of two independent sample variances taken from normal populations with equal variances is

an F distribution

To avoid the problem of not having access to Tables of F distribution with values given for the lower tail, the numerator of the test statistic should be the one with

the larger sample variance